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Variational principles, Surface Evolution, PDE's, level set methods and the Stereo Problem
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1999
"... We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equati ..."
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Cited by 193 (21 self)
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We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and vibility are presented on synthetic and real images.
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1990
"... this paper, we introduce a method for recovery of compact volumetric models for single part objects. To solve the shape recovery problem in isolation from segmentation, we assume that only a single object is present in the scene at a time. Although we made this simplification to break up the problem ..."
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Cited by 188 (5 self)
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this paper, we introduce a method for recovery of compact volumetric models for single part objects. To solve the shape recovery problem in isolation from segmentation, we assume that only a single object is present in the scene at a time. Although we made this simplification to break up the problem, this assumption is still valid for some restricted environments [30]. We show that the shape of those objects can be recovered subject to the model's internal constraints. In this work we use a partic ular example of compact volumetric modelssuperquad ric primitives with parametric deformations. We introduce a leastsquares minimization method to recover model and deformation parameters using range data as the input. Range data enables us to study shape recovery independent of different passive techniques of obtaining depth data, such as depth from stereo, depth from focus, or depth from motion. The fitting function which we min imize is a cost or energy function whose value depends on the distance of points from the model's surface and on the overall size of the model. We show that the solution space, which can have more than one "deep" minimum or acceptable solution and many shallow local minima, can be searched efficiently with a gradient descent method. By using a stochastic technique, the procedure can escape from shallow local minima, and a particular solution among several acceptable solutions can be reached by searching in a constrained parameter subspace. The paper is organized as follows. Section II is on parametric models in computer vision, focusing on comparison of generalized cylinders and superquadrics. Section III explains superquadric models in detail. Section IV is about recovery of nondeformed superquadric models, and Section V is on recovery of defo...
A SpaceSweep Approach to True MultiImage Matching
, 1996
"... The problem of determining feature correspondences across multiple views is considered. The term "true multiimage" matching is introduced to describe techniques that make full and efficient use of the geometric relationships between multiple images and the scene. A true multiimage technique must ge ..."
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Cited by 183 (4 self)
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The problem of determining feature correspondences across multiple views is considered. The term "true multiimage" matching is introduced to describe techniques that make full and efficient use of the geometric relationships between multiple images and the scene. A true multiimage technique must generalize to any number of images, be of linear algorithmic complexity in the number of images, and use all the images in an equal manner. A new spacesweep approach to true multiimage matching is presented that simultaneously determines 2D feature correspondences and the 3D positions of feature points in the scene. The method is based on the premise that areas of space where several viewing rays intersect are the likely locations of observed 3D scene features. It is shown that the intersections of viewing rays with a plane sweeping through space can be determined very efficiently, and a statistical model is developed to tell how likely it is that a given number of viewing rays will pass th...
Wavecluster: A multiresolution clustering approach for very large spatial databases
, 1998
"... Many applications require the management of spatial data. Clustering large spatial databases is an important problem which tries to find the densely populated regions in the feature space to be used in data mining, knowledge discovery, or efficient information retrieval. A good clustering approach s ..."
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Cited by 170 (5 self)
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Many applications require the management of spatial data. Clustering large spatial databases is an important problem which tries to find the densely populated regions in the feature space to be used in data mining, knowledge discovery, or efficient information retrieval. A good clustering approach should be efficient and detect clusters of arbitrary shape. It must be insensitive to the outliers (noise) and the order of input data. We propose WaveCluster, a novel clustering approach based on wavelet transforms, which satisfies all the above requirements. Using multiresolution property of wavelet transforms, we can effectively identify arbitrary shape clusters at different degrees of accuracy. We also demonstrate that WaveCluster is highly efficient in terms of time complexity. Experimental results on very large data sets are presented which show the efficiency and effectiveness of the proposed approach compared to the other recent clustering methods.
Removing Shadows from Images
 In ECCV 2002: European Conference on Computer Vision
, 2002
"... Abstract—This paper is concerned with the derivation of a progression of shadowfree image representations. First, we show that adopting certain assumptions about lights and cameras leads to a 1D, grayscale image representation which is illuminant invariant at each image pixel. We show that as a co ..."
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Cited by 168 (16 self)
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Abstract—This paper is concerned with the derivation of a progression of shadowfree image representations. First, we show that adopting certain assumptions about lights and cameras leads to a 1D, grayscale image representation which is illuminant invariant at each image pixel. We show that as a consequence, images represented in this form are shadowfree. We then extend this 1D representation to an equivalent 2D, chromaticity representation. We show that in this 2D representation, it is possible to relight all the image pixels in the same way, effectively deriving a 2D image representation which is additionally shadowfree. Finally, we show how to recover a 3D, full color shadowfree image representation by first (with the help of the 2D representation) identifying shadow edges. We then remove shadow edges from the edgemap of the original image by edge inpainting and we propose a method to reintegrate this thresholded edge map, thus deriving the soughtafter 3D shadowfree image. Index Terms—Shadow removal, illuminant invariance, reintegration. 1
Image Mosaicing for TeleReality Applications
, 1994
"... While a large number of virtual reality applications, such as fluid flow analysis and molecular modeling, deal with simulated data, many newer applications attempt to recreate true reality as convincingly as possible. Building detailed models for such applications, which we call telereality, is a m ..."
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Cited by 162 (12 self)
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While a large number of virtual reality applications, such as fluid flow analysis and molecular modeling, deal with simulated data, many newer applications attempt to recreate true reality as convincingly as possible. Building detailed models for such applications, which we call telereality, is a major bottleneck holding back their deployment. In this paper, we present techniques for automatically deriving realistic 2D scenes and 3D texturemapped models from video sequences, which can help overcome this bottleneck. The fundamental technique we use is image mosaicing, i.e., the automatic alignment of multiple images into larger aggregates which are then used to represent portions of a 3D scene. We begin with the easiest problems, those of flat scene and panoramic scene mosaicing, and progress to more complicated scenes, culminating in full 3D models. We also present a number of novel applications based on telereality technology.
On the geometry and algebra of the point and line correspondences between N images
, 1995
"... We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effect ..."
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Cited by 149 (6 self)
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We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We have a fairly complete picture of the situation in the case of points: there are only three types of algebraic relations which are satisfied by the coordinates of the images of a 3D point: bilinear relations arising when we consider pairs of images among the N and which are the wellknown epipolar constraints, trilinear relations arising when we consider triples of images among the N , and quadrilinear relations arising when we consider fourtuples of images among the N . In the case of lines, we show how the traditional perspective projection equation can be suitably generalized and that in the case of three images there exist two in...
Mixture Models for Optical Flow Computation
, 1993
"... The computahon of optical flow rehes on merg. ,ng znformat,on avadable over an zmage patch to form an estimate of D mage veloct!t at a point. Ths merging process rases a host of ssues, which include the treatment of outhers m component ve !oc*t!t measurements and the modehng of mulhple motions wath ..."
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Cited by 146 (16 self)
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The computahon of optical flow rehes on merg. ,ng znformat,on avadable over an zmage patch to form an estimate of D mage veloct!t at a point. Ths merging process rases a host of ssues, which include the treatment of outhers m component ve !oc*t!t measurements and the modehng of mulhple motions wathm a patch whzch arse from occlusion boundaries or transparency. We present a new ap proach for deahno wth these ssues. which s based Proc. CVPR'93, New York, June 1993 2 a c Figure 2: Multiple motion constraint lines for the region in Figure I (see text).
Relative Orientation
 International Journal of Computer Vision
, 1990
"... Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the in ..."
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Cited by 130 (2 self)
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Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the interpretation of binocular stereo information. Iterative methods for determining relative orientation were developed long ago; without them we would not have most of the topographic maps we do today. Relative orientation is also of importance in the recovery of motion and shape from an image sequence when successive frames are widely separated in time. Workers in motion vision are rediscovering some of the methods of photogrammetry. Described here is a simple iterative scheme for recovering relative orientation that, unlike existing methods, does not require a good initial guess for the baseline and the rotation. The data required is a pair of bundles of corresponding rays from the two projection centers to points in the scene. It is well known that at least five pairs of rays are needed. Less appears to be known about the existence of multiple solutions and their interpretation. These issues are discussed here. The unambiguous determination of all of the parameters of relative orientation is not possible when the observed points lie on a critical surface. These surfaces and their degenerate forms are analysed as well.
Map Learning with Uninterpreted Sensors and Effectors
 Artificial Intelligence
, 1997
"... This paper presents a set of methods by which a learning agent can learn a sequence of increasingly abstract and powerful interfaces to control a robot whose sensorimotor apparatus and environment are initially unknown. The result of the learning is a rich hierarchical model of the robot's world (it ..."
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Cited by 129 (20 self)
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This paper presents a set of methods by which a learning agent can learn a sequence of increasingly abstract and powerful interfaces to control a robot whose sensorimotor apparatus and environment are initially unknown. The result of the learning is a rich hierarchical model of the robot's world (its sensorimotor apparatus and environment). The learning methods rely on generic properties of the robot's world such as almosteverywhere smooth e ects of motor control signals on sensory features. At thelowest level of the hierarchy, the learning agent analyzes the e ects of its motor control signals in order to de ne a new set of control signals, one for each of the robot's degrees of freedom. It uses a generateandtest approach to de ne sensory features that capture important aspects of the environment. It uses linear regression to learn models that characterize contextdependent e ects of the control signals on the learned features. It uses these models to de ne highlevel control laws for nding and following paths de ned using constraints on the learned features. The agent abstracts these control laws, which interact with the continuous environment, to a nite set of actions that implement discrete state transitions. At this point, the agent has abstracted the robot's continuous world to a nitestate world and can use existing methods to learn its structure. The learning agent's methods are evaluated on several simulated robots with di erent sensorimotor systems and environments.